A general algorithm to design sets of all possible one dimensional unipolar orthogonal codes of same code length and weight

Abstract

This paper describe a general scheme to design all the uni-polar codes characterized by parameter (n, w). The binary sequence of length 'n' ('n' bits) and weight 'w' (number of bit '1's in the sequence) with its n-1 circular shifted versions represent the same code. These codes can be further put in different subsets characterized by (n, w, c a λ λ , ), where a λ and c λ are auto-correlation and crosscorrelation constraint respectively. All the codes within a set are called orthogonal to each other. In reality, they are pseudo orthogonal as cross-correlation is non-zero. With parameter (n, w, c a λ λ , ), there can be many sets each containing a number of orthogonal codes. All the codes in one set are always orthogonal to each other but not necessarily orthogonal to the codes in other sets. The code design scheme presented in this paper, can design all possible sets of codes. Users can select the code set as per their requirements. These uni-polar one dimensional orthogonal codes have their application in incoherent optical code division multiple access systems. The uni-polar optical orthogonal code can be generated by putting a single optical pulse at every position of bit '1' and no pulses at the positions of bit '0's in the sequence.

Optical orthogonal code generation scheme and grouping of codes for optical CDMA systems

“…In Optical CDMA (OCDMA) the spreading codes are binary unipolar symbols represented as f0; 1g. These spreading codes used in OCDMA are called optical orthogonal codes (OOC) or one-dimensional OOCs (1-D OOCs) (Chauhan et al 2010;Omrani and Vijay Kumar 2005).…”

“…. ; y nÀ1 Þ; where x t ; y t 2 ð0; 1Þ (Omrani and Vijay Kumar 2005;Chauhan et al 2010. for these codes rlk a !…”

“…The maximum number of OOC is given by Johnson bound (Omrani and Vijay Kumar 2005;Chauhan et al 2010;Chung et al 2015).…”

“…bxc denotes the largest integer value less then 'x' in eqn 3, 4, and 5 (Chauhan et al 2010;Omrani and Vijay Kumar 2005).…”

“…; B w ' here so edop matrix is of size ½w; w À 1. Equation 3.4 define how to calculate EDOP from DOP (Chauhan et al 2010) and flowchart is shown in Fig. 6 and process is shown in Fig.…”